Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0000972201\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.26027 | −1.59825 | −0.799126 | − | 0.601164i | \(-0.794704\pi\) | ||||
−0.799126 | + | 0.601164i | \(0.794704\pi\) | |||||||
\(3\) | 2.68549 | 1.55047 | 0.775235 | − | 0.631673i | \(-0.217631\pi\) | ||||
0.775235 | + | 0.631673i | \(0.217631\pi\) | |||||||
\(4\) | 3.10882 | 1.55441 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −6.06994 | −2.47804 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.50623 | −0.886086 | ||||||||
\(9\) | 4.21188 | 1.40396 | ||||||||
\(10\) | −2.26027 | −0.714760 | ||||||||
\(11\) | −4.01701 | −1.21117 | −0.605587 | − | 0.795779i | \(-0.707061\pi\) | ||||
−0.605587 | + | 0.795779i | \(0.707061\pi\) | |||||||
\(12\) | 8.34871 | 2.41007 | ||||||||
\(13\) | −3.92654 | −1.08903 | −0.544513 | − | 0.838752i | \(-0.683286\pi\) | ||||
−0.544513 | + | 0.838752i | \(0.683286\pi\) | |||||||
\(14\) | 2.26027 | 0.604082 | ||||||||
\(15\) | 2.68549 | 0.693392 | ||||||||
\(16\) | −0.552885 | −0.138221 | ||||||||
\(17\) | 0.783575 | 0.190045 | 0.0950224 | − | 0.995475i | \(-0.469708\pi\) | ||||
0.0950224 | + | 0.995475i | \(0.469708\pi\) | |||||||
\(18\) | −9.51998 | −2.24388 | ||||||||
\(19\) | 4.35807 | 0.999809 | 0.499905 | − | 0.866080i | \(-0.333368\pi\) | ||||
0.499905 | + | 0.866080i | \(0.333368\pi\) | |||||||
\(20\) | 3.10882 | 0.695153 | ||||||||
\(21\) | −2.68549 | −0.586023 | ||||||||
\(22\) | 9.07952 | 1.93576 | ||||||||
\(23\) | 5.35968 | 1.11757 | 0.558786 | − | 0.829312i | \(-0.311267\pi\) | ||||
0.558786 | + | 0.829312i | \(0.311267\pi\) | |||||||
\(24\) | −6.73046 | −1.37385 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 8.87504 | 1.74054 | ||||||||
\(27\) | 3.25449 | 0.626327 | ||||||||
\(28\) | −3.10882 | −0.587511 | ||||||||
\(29\) | 0.420322 | 0.0780518 | 0.0390259 | − | 0.999238i | \(-0.487575\pi\) | ||||
0.0390259 | + | 0.999238i | \(0.487575\pi\) | |||||||
\(30\) | −6.06994 | −1.10821 | ||||||||
\(31\) | −3.30251 | −0.593148 | −0.296574 | − | 0.955010i | \(-0.595844\pi\) | ||||
−0.296574 | + | 0.955010i | \(0.595844\pi\) | |||||||
\(32\) | 6.26213 | 1.10700 | ||||||||
\(33\) | −10.7876 | −1.87789 | ||||||||
\(34\) | −1.77109 | −0.303739 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 13.0940 | 2.18233 | ||||||||
\(37\) | 3.98055 | 0.654398 | 0.327199 | − | 0.944955i | \(-0.393895\pi\) | ||||
0.327199 | + | 0.944955i | \(0.393895\pi\) | |||||||
\(38\) | −9.85041 | −1.59795 | ||||||||
\(39\) | −10.5447 | −1.68850 | ||||||||
\(40\) | −2.50623 | −0.396270 | ||||||||
\(41\) | −5.55746 | −0.867930 | −0.433965 | − | 0.900930i | \(-0.642886\pi\) | ||||
−0.433965 | + | 0.900930i | \(0.642886\pi\) | |||||||
\(42\) | 6.06994 | 0.936612 | ||||||||
\(43\) | −9.62469 | −1.46775 | −0.733876 | − | 0.679284i | \(-0.762290\pi\) | ||||
−0.733876 | + | 0.679284i | \(0.762290\pi\) | |||||||
\(44\) | −12.4881 | −1.88266 | ||||||||
\(45\) | 4.21188 | 0.627870 | ||||||||
\(46\) | −12.1143 | −1.78616 | ||||||||
\(47\) | −3.60160 | −0.525347 | −0.262673 | − | 0.964885i | \(-0.584604\pi\) | ||||
−0.262673 | + | 0.964885i | \(0.584604\pi\) | |||||||
\(48\) | −1.48477 | −0.214308 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.26027 | −0.319650 | ||||||||
\(51\) | 2.10428 | 0.294659 | ||||||||
\(52\) | −12.2069 | −1.69279 | ||||||||
\(53\) | −6.21293 | −0.853411 | −0.426706 | − | 0.904391i | \(-0.640326\pi\) | ||||
−0.426706 | + | 0.904391i | \(0.640326\pi\) | |||||||
\(54\) | −7.35603 | −1.00103 | ||||||||
\(55\) | −4.01701 | −0.541653 | ||||||||
\(56\) | 2.50623 | 0.334909 | ||||||||
\(57\) | 11.7036 | 1.55018 | ||||||||
\(58\) | −0.950041 | −0.124746 | ||||||||
\(59\) | 1.38397 | 0.180178 | 0.0900889 | − | 0.995934i | \(-0.471285\pi\) | ||||
0.0900889 | + | 0.995934i | \(0.471285\pi\) | |||||||
\(60\) | 8.34871 | 1.07781 | ||||||||
\(61\) | 5.60897 | 0.718154 | 0.359077 | − | 0.933308i | \(-0.383091\pi\) | ||||
0.359077 | + | 0.933308i | \(0.383091\pi\) | |||||||
\(62\) | 7.46455 | 0.947999 | ||||||||
\(63\) | −4.21188 | −0.530647 | ||||||||
\(64\) | −13.0483 | −1.63104 | ||||||||
\(65\) | −3.92654 | −0.487027 | ||||||||
\(66\) | 24.3830 | 3.00134 | ||||||||
\(67\) | −11.6655 | −1.42516 | −0.712582 | − | 0.701589i | \(-0.752474\pi\) | ||||
−0.712582 | + | 0.701589i | \(0.752474\pi\) | |||||||
\(68\) | 2.43599 | 0.295407 | ||||||||
\(69\) | 14.3934 | 1.73276 | ||||||||
\(70\) | 2.26027 | 0.270154 | ||||||||
\(71\) | −7.98094 | −0.947163 | −0.473582 | − | 0.880750i | \(-0.657039\pi\) | ||||
−0.473582 | + | 0.880750i | \(0.657039\pi\) | |||||||
\(72\) | −10.5559 | −1.24403 | ||||||||
\(73\) | 8.23419 | 0.963739 | 0.481869 | − | 0.876243i | \(-0.339958\pi\) | ||||
0.481869 | + | 0.876243i | \(0.339958\pi\) | |||||||
\(74\) | −8.99711 | −1.04589 | ||||||||
\(75\) | 2.68549 | 0.310094 | ||||||||
\(76\) | 13.5484 | 1.55411 | ||||||||
\(77\) | 4.01701 | 0.457780 | ||||||||
\(78\) | 23.8339 | 2.69865 | ||||||||
\(79\) | 9.36876 | 1.05407 | 0.527034 | − | 0.849844i | \(-0.323304\pi\) | ||||
0.527034 | + | 0.849844i | \(0.323304\pi\) | |||||||
\(80\) | −0.552885 | −0.0618144 | ||||||||
\(81\) | −3.89572 | −0.432858 | ||||||||
\(82\) | 12.5614 | 1.38717 | ||||||||
\(83\) | −6.12838 | −0.672677 | −0.336339 | − | 0.941741i | \(-0.609189\pi\) | ||||
−0.336339 | + | 0.941741i | \(0.609189\pi\) | |||||||
\(84\) | −8.34871 | −0.910919 | ||||||||
\(85\) | 0.783575 | 0.0849906 | ||||||||
\(86\) | 21.7544 | 2.34584 | ||||||||
\(87\) | 1.12877 | 0.121017 | ||||||||
\(88\) | 10.0675 | 1.07320 | ||||||||
\(89\) | −14.0744 | −1.49188 | −0.745940 | − | 0.666013i | \(-0.767999\pi\) | ||||
−0.745940 | + | 0.666013i | \(0.767999\pi\) | |||||||
\(90\) | −9.51998 | −1.00349 | ||||||||
\(91\) | 3.92654 | 0.411613 | ||||||||
\(92\) | 16.6623 | 1.73716 | ||||||||
\(93\) | −8.86886 | −0.919658 | ||||||||
\(94\) | 8.14058 | 0.839637 | ||||||||
\(95\) | 4.35807 | 0.447128 | ||||||||
\(96\) | 16.8169 | 1.71637 | ||||||||
\(97\) | 4.45892 | 0.452735 | 0.226368 | − | 0.974042i | \(-0.427315\pi\) | ||||
0.226368 | + | 0.974042i | \(0.427315\pi\) | |||||||
\(98\) | −2.26027 | −0.228322 | ||||||||
\(99\) | −16.9191 | −1.70044 | ||||||||
\(100\) | 3.10882 | 0.310882 | ||||||||
\(101\) | 5.22163 | 0.519572 | 0.259786 | − | 0.965666i | \(-0.416348\pi\) | ||||
0.259786 | + | 0.965666i | \(0.416348\pi\) | |||||||
\(102\) | −4.75625 | −0.470939 | ||||||||
\(103\) | −8.15389 | −0.803426 | −0.401713 | − | 0.915766i | \(-0.631585\pi\) | ||||
−0.401713 | + | 0.915766i | \(0.631585\pi\) | |||||||
\(104\) | 9.84081 | 0.964970 | ||||||||
\(105\) | −2.68549 | −0.262077 | ||||||||
\(106\) | 14.0429 | 1.36397 | ||||||||
\(107\) | 7.51255 | 0.726266 | 0.363133 | − | 0.931737i | \(-0.381707\pi\) | ||||
0.363133 | + | 0.931737i | \(0.381707\pi\) | |||||||
\(108\) | 10.1176 | 0.973568 | ||||||||
\(109\) | −8.18571 | −0.784049 | −0.392025 | − | 0.919955i | \(-0.628225\pi\) | ||||
−0.392025 | + | 0.919955i | \(0.628225\pi\) | |||||||
\(110\) | 9.07952 | 0.865698 | ||||||||
\(111\) | 10.6897 | 1.01462 | ||||||||
\(112\) | 0.552885 | 0.0522427 | ||||||||
\(113\) | 4.35144 | 0.409349 | 0.204675 | − | 0.978830i | \(-0.434386\pi\) | ||||
0.204675 | + | 0.978830i | \(0.434386\pi\) | |||||||
\(114\) | −26.4532 | −2.47757 | ||||||||
\(115\) | 5.35968 | 0.499793 | ||||||||
\(116\) | 1.30670 | 0.121324 | ||||||||
\(117\) | −16.5381 | −1.52895 | ||||||||
\(118\) | −3.12815 | −0.287970 | ||||||||
\(119\) | −0.783575 | −0.0718302 | ||||||||
\(120\) | −6.73046 | −0.614404 | ||||||||
\(121\) | 5.13635 | 0.466940 | ||||||||
\(122\) | −12.6778 | −1.14779 | ||||||||
\(123\) | −14.9245 | −1.34570 | ||||||||
\(124\) | −10.2669 | −0.921994 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 9.51998 | 0.848107 | ||||||||
\(127\) | 11.9367 | 1.05921 | 0.529607 | − | 0.848243i | \(-0.322339\pi\) | ||||
0.529607 | + | 0.848243i | \(0.322339\pi\) | |||||||
\(128\) | 16.9685 | 1.49982 | ||||||||
\(129\) | −25.8470 | −2.27571 | ||||||||
\(130\) | 8.87504 | 0.778392 | ||||||||
\(131\) | 2.16050 | 0.188764 | 0.0943818 | − | 0.995536i | \(-0.469913\pi\) | ||||
0.0943818 | + | 0.995536i | \(0.469913\pi\) | |||||||
\(132\) | −33.5368 | −2.91901 | ||||||||
\(133\) | −4.35807 | −0.377892 | ||||||||
\(134\) | 26.3671 | 2.27777 | ||||||||
\(135\) | 3.25449 | 0.280102 | ||||||||
\(136\) | −1.96382 | −0.168396 | ||||||||
\(137\) | −16.3714 | −1.39871 | −0.699353 | − | 0.714776i | \(-0.746528\pi\) | ||||
−0.699353 | + | 0.714776i | \(0.746528\pi\) | |||||||
\(138\) | −32.5330 | −2.76939 | ||||||||
\(139\) | −0.0524197 | −0.00444618 | −0.00222309 | − | 0.999998i | \(-0.500708\pi\) | ||||
−0.00222309 | + | 0.999998i | \(0.500708\pi\) | |||||||
\(140\) | −3.10882 | −0.262743 | ||||||||
\(141\) | −9.67207 | −0.814535 | ||||||||
\(142\) | 18.0391 | 1.51381 | ||||||||
\(143\) | 15.7729 | 1.31900 | ||||||||
\(144\) | −2.32868 | −0.194057 | ||||||||
\(145\) | 0.420322 | 0.0349058 | ||||||||
\(146\) | −18.6115 | −1.54030 | ||||||||
\(147\) | 2.68549 | 0.221496 | ||||||||
\(148\) | 12.3748 | 1.01720 | ||||||||
\(149\) | −12.0693 | −0.988757 | −0.494379 | − | 0.869247i | \(-0.664604\pi\) | ||||
−0.494379 | + | 0.869247i | \(0.664604\pi\) | |||||||
\(150\) | −6.06994 | −0.495609 | ||||||||
\(151\) | 5.20223 | 0.423351 | 0.211676 | − | 0.977340i | \(-0.432108\pi\) | ||||
0.211676 | + | 0.977340i | \(0.432108\pi\) | |||||||
\(152\) | −10.9223 | −0.885917 | ||||||||
\(153\) | 3.30032 | 0.266815 | ||||||||
\(154\) | −9.07952 | −0.731648 | ||||||||
\(155\) | −3.30251 | −0.265264 | ||||||||
\(156\) | −32.7816 | −2.62462 | ||||||||
\(157\) | −17.8568 | −1.42513 | −0.712563 | − | 0.701608i | \(-0.752466\pi\) | ||||
−0.712563 | + | 0.701608i | \(0.752466\pi\) | |||||||
\(158\) | −21.1759 | −1.68467 | ||||||||
\(159\) | −16.6848 | −1.32319 | ||||||||
\(160\) | 6.26213 | 0.495065 | ||||||||
\(161\) | −5.35968 | −0.422402 | ||||||||
\(162\) | 8.80537 | 0.691816 | ||||||||
\(163\) | −2.26610 | −0.177494 | −0.0887472 | − | 0.996054i | \(-0.528286\pi\) | ||||
−0.0887472 | + | 0.996054i | \(0.528286\pi\) | |||||||
\(164\) | −17.2771 | −1.34912 | ||||||||
\(165\) | −10.7876 | −0.839817 | ||||||||
\(166\) | 13.8518 | 1.07511 | ||||||||
\(167\) | 14.5885 | 1.12889 | 0.564445 | − | 0.825471i | \(-0.309090\pi\) | ||||
0.564445 | + | 0.825471i | \(0.309090\pi\) | |||||||
\(168\) | 6.73046 | 0.519266 | ||||||||
\(169\) | 2.41771 | 0.185978 | ||||||||
\(170\) | −1.77109 | −0.135836 | ||||||||
\(171\) | 18.3557 | 1.40369 | ||||||||
\(172\) | −29.9214 | −2.28149 | ||||||||
\(173\) | −7.71858 | −0.586833 | −0.293416 | − | 0.955985i | \(-0.594792\pi\) | ||||
−0.293416 | + | 0.955985i | \(0.594792\pi\) | |||||||
\(174\) | −2.55133 | −0.193416 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 2.22094 | 0.167410 | ||||||||
\(177\) | 3.71665 | 0.279360 | ||||||||
\(178\) | 31.8119 | 2.38440 | ||||||||
\(179\) | 21.2291 | 1.58674 | 0.793369 | − | 0.608741i | \(-0.208325\pi\) | ||||
0.793369 | + | 0.608741i | \(0.208325\pi\) | |||||||
\(180\) | 13.0940 | 0.975966 | ||||||||
\(181\) | −6.16803 | −0.458466 | −0.229233 | − | 0.973372i | \(-0.573622\pi\) | ||||
−0.229233 | + | 0.973372i | \(0.573622\pi\) | |||||||
\(182\) | −8.87504 | −0.657862 | ||||||||
\(183\) | 15.0628 | 1.11348 | ||||||||
\(184\) | −13.4326 | −0.990264 | ||||||||
\(185\) | 3.98055 | 0.292656 | ||||||||
\(186\) | 20.0460 | 1.46985 | ||||||||
\(187\) | −3.14762 | −0.230177 | ||||||||
\(188\) | −11.1967 | −0.816604 | ||||||||
\(189\) | −3.25449 | −0.236729 | ||||||||
\(190\) | −9.85041 | −0.714624 | ||||||||
\(191\) | −13.9291 | −1.00788 | −0.503938 | − | 0.863740i | \(-0.668116\pi\) | ||||
−0.503938 | + | 0.863740i | \(0.668116\pi\) | |||||||
\(192\) | −35.0412 | −2.52888 | ||||||||
\(193\) | −16.4152 | −1.18159 | −0.590797 | − | 0.806820i | \(-0.701187\pi\) | ||||
−0.590797 | + | 0.806820i | \(0.701187\pi\) | |||||||
\(194\) | −10.0784 | −0.723585 | ||||||||
\(195\) | −10.5447 | −0.755122 | ||||||||
\(196\) | 3.10882 | 0.222058 | ||||||||
\(197\) | 10.6128 | 0.756134 | 0.378067 | − | 0.925778i | \(-0.376589\pi\) | ||||
0.378067 | + | 0.925778i | \(0.376589\pi\) | |||||||
\(198\) | 38.2418 | 2.71773 | ||||||||
\(199\) | −23.0594 | −1.63464 | −0.817320 | − | 0.576185i | \(-0.804541\pi\) | ||||
−0.817320 | + | 0.576185i | \(0.804541\pi\) | |||||||
\(200\) | −2.50623 | −0.177217 | ||||||||
\(201\) | −31.3275 | −2.20967 | ||||||||
\(202\) | −11.8023 | −0.830406 | ||||||||
\(203\) | −0.420322 | −0.0295008 | ||||||||
\(204\) | 6.54184 | 0.458020 | ||||||||
\(205\) | −5.55746 | −0.388150 | ||||||||
\(206\) | 18.4300 | 1.28408 | ||||||||
\(207\) | 22.5743 | 1.56902 | ||||||||
\(208\) | 2.17092 | 0.150527 | ||||||||
\(209\) | −17.5064 | −1.21094 | ||||||||
\(210\) | 6.06994 | 0.418866 | ||||||||
\(211\) | 6.54981 | 0.450908 | 0.225454 | − | 0.974254i | \(-0.427614\pi\) | ||||
0.225454 | + | 0.974254i | \(0.427614\pi\) | |||||||
\(212\) | −19.3149 | −1.32655 | ||||||||
\(213\) | −21.4328 | −1.46855 | ||||||||
\(214\) | −16.9804 | −1.16076 | ||||||||
\(215\) | −9.62469 | −0.656398 | ||||||||
\(216\) | −8.15650 | −0.554979 | ||||||||
\(217\) | 3.30251 | 0.224189 | ||||||||
\(218\) | 18.5019 | 1.25311 | ||||||||
\(219\) | 22.1129 | 1.49425 | ||||||||
\(220\) | −12.4881 | −0.841951 | ||||||||
\(221\) | −3.07674 | −0.206964 | ||||||||
\(222\) | −24.1617 | −1.62163 | ||||||||
\(223\) | −10.1359 | −0.678749 | −0.339374 | − | 0.940651i | \(-0.610215\pi\) | ||||
−0.339374 | + | 0.940651i | \(0.610215\pi\) | |||||||
\(224\) | −6.26213 | −0.418406 | ||||||||
\(225\) | 4.21188 | 0.280792 | ||||||||
\(226\) | −9.83543 | −0.654243 | ||||||||
\(227\) | 15.5838 | 1.03433 | 0.517165 | − | 0.855886i | \(-0.326987\pi\) | ||||
0.517165 | + | 0.855886i | \(0.326987\pi\) | |||||||
\(228\) | 36.3843 | 2.40961 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −12.1143 | −0.798795 | ||||||||
\(231\) | 10.7876 | 0.709775 | ||||||||
\(232\) | −1.05342 | −0.0691606 | ||||||||
\(233\) | 15.4652 | 1.01316 | 0.506581 | − | 0.862192i | \(-0.330909\pi\) | ||||
0.506581 | + | 0.862192i | \(0.330909\pi\) | |||||||
\(234\) | 37.3806 | 2.44364 | ||||||||
\(235\) | −3.60160 | −0.234942 | ||||||||
\(236\) | 4.30252 | 0.280070 | ||||||||
\(237\) | 25.1597 | 1.63430 | ||||||||
\(238\) | 1.77109 | 0.114803 | ||||||||
\(239\) | −17.8054 | −1.15174 | −0.575869 | − | 0.817542i | \(-0.695336\pi\) | ||||
−0.575869 | + | 0.817542i | \(0.695336\pi\) | |||||||
\(240\) | −1.48477 | −0.0958414 | ||||||||
\(241\) | −4.03384 | −0.259842 | −0.129921 | − | 0.991524i | \(-0.541472\pi\) | ||||
−0.129921 | + | 0.991524i | \(0.541472\pi\) | |||||||
\(242\) | −11.6095 | −0.746289 | ||||||||
\(243\) | −20.2254 | −1.29746 | ||||||||
\(244\) | 17.4373 | 1.11631 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 33.7335 | 2.15077 | ||||||||
\(247\) | −17.1121 | −1.08882 | ||||||||
\(248\) | 8.27684 | 0.525580 | ||||||||
\(249\) | −16.4577 | −1.04297 | ||||||||
\(250\) | −2.26027 | −0.142952 | ||||||||
\(251\) | −5.86197 | −0.370004 | −0.185002 | − | 0.982738i | \(-0.559229\pi\) | ||||
−0.185002 | + | 0.982738i | \(0.559229\pi\) | |||||||
\(252\) | −13.0940 | −0.824842 | ||||||||
\(253\) | −21.5299 | −1.35357 | ||||||||
\(254\) | −26.9803 | −1.69289 | ||||||||
\(255\) | 2.10428 | 0.131775 | ||||||||
\(256\) | −12.2567 | −0.766043 | ||||||||
\(257\) | 27.2256 | 1.69829 | 0.849144 | − | 0.528161i | \(-0.177118\pi\) | ||||
0.849144 | + | 0.528161i | \(0.177118\pi\) | |||||||
\(258\) | 58.4213 | 3.63715 | ||||||||
\(259\) | −3.98055 | −0.247339 | ||||||||
\(260\) | −12.2069 | −0.757040 | ||||||||
\(261\) | 1.77034 | 0.109582 | ||||||||
\(262\) | −4.88331 | −0.301692 | ||||||||
\(263\) | −5.20255 | −0.320803 | −0.160402 | − | 0.987052i | \(-0.551279\pi\) | ||||
−0.160402 | + | 0.987052i | \(0.551279\pi\) | |||||||
\(264\) | 27.0363 | 1.66397 | ||||||||
\(265\) | −6.21293 | −0.381657 | ||||||||
\(266\) | 9.85041 | 0.603967 | ||||||||
\(267\) | −37.7966 | −2.31312 | ||||||||
\(268\) | −36.2658 | −2.21529 | ||||||||
\(269\) | 27.8485 | 1.69795 | 0.848976 | − | 0.528431i | \(-0.177219\pi\) | ||||
0.848976 | + | 0.528431i | \(0.177219\pi\) | |||||||
\(270\) | −7.35603 | −0.447673 | ||||||||
\(271\) | −26.0266 | −1.58100 | −0.790501 | − | 0.612460i | \(-0.790180\pi\) | ||||
−0.790501 | + | 0.612460i | \(0.790180\pi\) | |||||||
\(272\) | −0.433227 | −0.0262682 | ||||||||
\(273\) | 10.5447 | 0.638194 | ||||||||
\(274\) | 37.0039 | 2.23548 | ||||||||
\(275\) | −4.01701 | −0.242235 | ||||||||
\(276\) | 44.7465 | 2.69342 | ||||||||
\(277\) | −23.5463 | −1.41476 | −0.707379 | − | 0.706834i | \(-0.750123\pi\) | ||||
−0.707379 | + | 0.706834i | \(0.750123\pi\) | |||||||
\(278\) | 0.118483 | 0.00710611 | ||||||||
\(279\) | −13.9098 | −0.832755 | ||||||||
\(280\) | 2.50623 | 0.149776 | ||||||||
\(281\) | 8.18227 | 0.488113 | 0.244057 | − | 0.969761i | \(-0.421522\pi\) | ||||
0.244057 | + | 0.969761i | \(0.421522\pi\) | |||||||
\(282\) | 21.8615 | 1.30183 | ||||||||
\(283\) | 19.5497 | 1.16211 | 0.581055 | − | 0.813865i | \(-0.302640\pi\) | ||||
0.581055 | + | 0.813865i | \(0.302640\pi\) | |||||||
\(284\) | −24.8113 | −1.47228 | ||||||||
\(285\) | 11.7036 | 0.693259 | ||||||||
\(286\) | −35.6511 | −2.10809 | ||||||||
\(287\) | 5.55746 | 0.328047 | ||||||||
\(288\) | 26.3753 | 1.55418 | ||||||||
\(289\) | −16.3860 | −0.963883 | ||||||||
\(290\) | −0.950041 | −0.0557883 | ||||||||
\(291\) | 11.9744 | 0.701952 | ||||||||
\(292\) | 25.5986 | 1.49804 | ||||||||
\(293\) | 3.49094 | 0.203943 | 0.101971 | − | 0.994787i | \(-0.467485\pi\) | ||||
0.101971 | + | 0.994787i | \(0.467485\pi\) | |||||||
\(294\) | −6.06994 | −0.354006 | ||||||||
\(295\) | 1.38397 | 0.0805780 | ||||||||
\(296\) | −9.97616 | −0.579853 | ||||||||
\(297\) | −13.0733 | −0.758590 | ||||||||
\(298\) | 27.2799 | 1.58028 | ||||||||
\(299\) | −21.0450 | −1.21706 | ||||||||
\(300\) | 8.34871 | 0.482013 | ||||||||
\(301\) | 9.62469 | 0.554758 | ||||||||
\(302\) | −11.7584 | −0.676622 | ||||||||
\(303\) | 14.0227 | 0.805581 | ||||||||
\(304\) | −2.40951 | −0.138195 | ||||||||
\(305\) | 5.60897 | 0.321168 | ||||||||
\(306\) | −7.45961 | −0.426438 | ||||||||
\(307\) | −25.6441 | −1.46359 | −0.731793 | − | 0.681527i | \(-0.761316\pi\) | ||||
−0.731793 | + | 0.681527i | \(0.761316\pi\) | |||||||
\(308\) | 12.4881 | 0.711578 | ||||||||
\(309\) | −21.8972 | −1.24569 | ||||||||
\(310\) | 7.46455 | 0.423958 | ||||||||
\(311\) | −31.5865 | −1.79111 | −0.895553 | − | 0.444956i | \(-0.853219\pi\) | ||||
−0.895553 | + | 0.444956i | \(0.853219\pi\) | |||||||
\(312\) | 26.4274 | 1.49616 | ||||||||
\(313\) | 3.12003 | 0.176354 | 0.0881771 | − | 0.996105i | \(-0.471896\pi\) | ||||
0.0881771 | + | 0.996105i | \(0.471896\pi\) | |||||||
\(314\) | 40.3611 | 2.27771 | ||||||||
\(315\) | −4.21188 | −0.237312 | ||||||||
\(316\) | 29.1258 | 1.63845 | ||||||||
\(317\) | −35.3159 | −1.98354 | −0.991770 | − | 0.128031i | \(-0.959134\pi\) | ||||
−0.991770 | + | 0.128031i | \(0.959134\pi\) | |||||||
\(318\) | 37.7121 | 2.11479 | ||||||||
\(319\) | −1.68844 | −0.0945343 | ||||||||
\(320\) | −13.0483 | −0.729423 | ||||||||
\(321\) | 20.1749 | 1.12605 | ||||||||
\(322\) | 12.1143 | 0.675105 | ||||||||
\(323\) | 3.41487 | 0.190009 | ||||||||
\(324\) | −12.1111 | −0.672838 | ||||||||
\(325\) | −3.92654 | −0.217805 | ||||||||
\(326\) | 5.12199 | 0.283681 | ||||||||
\(327\) | −21.9827 | −1.21564 | ||||||||
\(328\) | 13.9283 | 0.769060 | ||||||||
\(329\) | 3.60160 | 0.198562 | ||||||||
\(330\) | 24.3830 | 1.34224 | ||||||||
\(331\) | −13.4697 | −0.740364 | −0.370182 | − | 0.928959i | \(-0.620705\pi\) | ||||
−0.370182 | + | 0.928959i | \(0.620705\pi\) | |||||||
\(332\) | −19.0520 | −1.04562 | ||||||||
\(333\) | 16.7656 | 0.918748 | ||||||||
\(334\) | −32.9739 | −1.80425 | ||||||||
\(335\) | −11.6655 | −0.637353 | ||||||||
\(336\) | 1.48477 | 0.0810008 | ||||||||
\(337\) | −19.0841 | −1.03958 | −0.519788 | − | 0.854295i | \(-0.673989\pi\) | ||||
−0.519788 | + | 0.854295i | \(0.673989\pi\) | |||||||
\(338\) | −5.46468 | −0.297240 | ||||||||
\(339\) | 11.6858 | 0.634684 | ||||||||
\(340\) | 2.43599 | 0.132110 | ||||||||
\(341\) | 13.2662 | 0.718405 | ||||||||
\(342\) | −41.4887 | −2.24345 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 24.1217 | 1.30055 | ||||||||
\(345\) | 14.3934 | 0.774915 | ||||||||
\(346\) | 17.4461 | 0.937906 | ||||||||
\(347\) | 4.70667 | 0.252667 | 0.126334 | − | 0.991988i | \(-0.459679\pi\) | ||||
0.126334 | + | 0.991988i | \(0.459679\pi\) | |||||||
\(348\) | 3.50915 | 0.188110 | ||||||||
\(349\) | −23.2971 | −1.24707 | −0.623533 | − | 0.781797i | \(-0.714303\pi\) | ||||
−0.623533 | + | 0.781797i | \(0.714303\pi\) | |||||||
\(350\) | 2.26027 | 0.120816 | ||||||||
\(351\) | −12.7789 | −0.682086 | ||||||||
\(352\) | −25.1550 | −1.34077 | ||||||||
\(353\) | 11.2597 | 0.599292 | 0.299646 | − | 0.954050i | \(-0.403131\pi\) | ||||
0.299646 | + | 0.954050i | \(0.403131\pi\) | |||||||
\(354\) | −8.40063 | −0.446488 | ||||||||
\(355\) | −7.98094 | −0.423584 | ||||||||
\(356\) | −43.7547 | −2.31899 | ||||||||
\(357\) | −2.10428 | −0.111371 | ||||||||
\(358\) | −47.9835 | −2.53601 | ||||||||
\(359\) | 16.8795 | 0.890865 | 0.445433 | − | 0.895316i | \(-0.353050\pi\) | ||||
0.445433 | + | 0.895316i | \(0.353050\pi\) | |||||||
\(360\) | −10.5559 | −0.556346 | ||||||||
\(361\) | −0.00724108 | −0.000381110 0 | ||||||||
\(362\) | 13.9414 | 0.732744 | ||||||||
\(363\) | 13.7936 | 0.723978 | ||||||||
\(364\) | 12.2069 | 0.639815 | ||||||||
\(365\) | 8.23419 | 0.430997 | ||||||||
\(366\) | −34.0461 | −1.77962 | ||||||||
\(367\) | −13.0510 | −0.681259 | −0.340629 | − | 0.940198i | \(-0.610640\pi\) | ||||
−0.340629 | + | 0.940198i | \(0.610640\pi\) | |||||||
\(368\) | −2.96329 | −0.154472 | ||||||||
\(369\) | −23.4074 | −1.21854 | ||||||||
\(370\) | −8.99711 | −0.467737 | ||||||||
\(371\) | 6.21293 | 0.322559 | ||||||||
\(372\) | −27.5717 | −1.42952 | ||||||||
\(373\) | −8.22658 | −0.425956 | −0.212978 | − | 0.977057i | \(-0.568316\pi\) | ||||
−0.212978 | + | 0.977057i | \(0.568316\pi\) | |||||||
\(374\) | 7.11448 | 0.367881 | ||||||||
\(375\) | 2.68549 | 0.138678 | ||||||||
\(376\) | 9.02642 | 0.465502 | ||||||||
\(377\) | −1.65041 | −0.0850005 | ||||||||
\(378\) | 7.35603 | 0.378353 | ||||||||
\(379\) | −14.9967 | −0.770329 | −0.385164 | − | 0.922848i | \(-0.625855\pi\) | ||||
−0.385164 | + | 0.922848i | \(0.625855\pi\) | |||||||
\(380\) | 13.5484 | 0.695020 | ||||||||
\(381\) | 32.0561 | 1.64228 | ||||||||
\(382\) | 31.4836 | 1.61084 | ||||||||
\(383\) | 5.95662 | 0.304369 | 0.152185 | − | 0.988352i | \(-0.451369\pi\) | ||||
0.152185 | + | 0.988352i | \(0.451369\pi\) | |||||||
\(384\) | 45.5687 | 2.32542 | ||||||||
\(385\) | 4.01701 | 0.204726 | ||||||||
\(386\) | 37.1029 | 1.88849 | ||||||||
\(387\) | −40.5380 | −2.06066 | ||||||||
\(388\) | 13.8620 | 0.703736 | ||||||||
\(389\) | 9.33318 | 0.473211 | 0.236606 | − | 0.971606i | \(-0.423965\pi\) | ||||
0.236606 | + | 0.971606i | \(0.423965\pi\) | |||||||
\(390\) | 23.8339 | 1.20687 | ||||||||
\(391\) | 4.19971 | 0.212389 | ||||||||
\(392\) | −2.50623 | −0.126584 | ||||||||
\(393\) | 5.80200 | 0.292672 | ||||||||
\(394\) | −23.9879 | −1.20849 | ||||||||
\(395\) | 9.36876 | 0.471393 | ||||||||
\(396\) | −52.5985 | −2.64318 | ||||||||
\(397\) | −23.0054 | −1.15461 | −0.577305 | − | 0.816529i | \(-0.695896\pi\) | ||||
−0.577305 | + | 0.816529i | \(0.695896\pi\) | |||||||
\(398\) | 52.1205 | 2.61257 | ||||||||
\(399\) | −11.7036 | −0.585911 | ||||||||
\(400\) | −0.552885 | −0.0276442 | ||||||||
\(401\) | 2.59903 | 0.129789 | 0.0648947 | − | 0.997892i | \(-0.479329\pi\) | ||||
0.0648947 | + | 0.997892i | \(0.479329\pi\) | |||||||
\(402\) | 70.8087 | 3.53162 | ||||||||
\(403\) | 12.9674 | 0.645953 | ||||||||
\(404\) | 16.2331 | 0.807627 | ||||||||
\(405\) | −3.89572 | −0.193580 | ||||||||
\(406\) | 0.950041 | 0.0471497 | ||||||||
\(407\) | −15.9899 | −0.792589 | ||||||||
\(408\) | −5.27382 | −0.261093 | ||||||||
\(409\) | −6.26569 | −0.309819 | −0.154909 | − | 0.987929i | \(-0.549509\pi\) | ||||
−0.154909 | + | 0.987929i | \(0.549509\pi\) | |||||||
\(410\) | 12.5614 | 0.620362 | ||||||||
\(411\) | −43.9654 | −2.16865 | ||||||||
\(412\) | −25.3490 | −1.24885 | ||||||||
\(413\) | −1.38397 | −0.0681008 | ||||||||
\(414\) | −51.0241 | −2.50770 | ||||||||
\(415\) | −6.12838 | −0.300830 | ||||||||
\(416\) | −24.5885 | −1.20555 | ||||||||
\(417\) | −0.140773 | −0.00689367 | ||||||||
\(418\) | 39.5692 | 1.93539 | ||||||||
\(419\) | −10.7933 | −0.527288 | −0.263644 | − | 0.964620i | \(-0.584924\pi\) | ||||
−0.263644 | + | 0.964620i | \(0.584924\pi\) | |||||||
\(420\) | −8.34871 | −0.407375 | ||||||||
\(421\) | 20.4635 | 0.997330 | 0.498665 | − | 0.866795i | \(-0.333824\pi\) | ||||
0.498665 | + | 0.866795i | \(0.333824\pi\) | |||||||
\(422\) | −14.8043 | −0.720664 | ||||||||
\(423\) | −15.1695 | −0.737566 | ||||||||
\(424\) | 15.5710 | 0.756195 | ||||||||
\(425\) | 0.783575 | 0.0380090 | ||||||||
\(426\) | 48.4438 | 2.34711 | ||||||||
\(427\) | −5.60897 | −0.271437 | ||||||||
\(428\) | 23.3552 | 1.12891 | ||||||||
\(429\) | 42.3581 | 2.04507 | ||||||||
\(430\) | 21.7544 | 1.04909 | ||||||||
\(431\) | 2.95172 | 0.142179 | 0.0710897 | − | 0.997470i | \(-0.477352\pi\) | ||||
0.0710897 | + | 0.997470i | \(0.477352\pi\) | |||||||
\(432\) | −1.79936 | −0.0865717 | ||||||||
\(433\) | 14.1747 | 0.681193 | 0.340596 | − | 0.940210i | \(-0.389371\pi\) | ||||
0.340596 | + | 0.940210i | \(0.389371\pi\) | |||||||
\(434\) | −7.46455 | −0.358310 | ||||||||
\(435\) | 1.12877 | 0.0541205 | ||||||||
\(436\) | −25.4479 | −1.21873 | ||||||||
\(437\) | 23.3579 | 1.11736 | ||||||||
\(438\) | −49.9810 | −2.38819 | ||||||||
\(439\) | −5.18949 | −0.247681 | −0.123841 | − | 0.992302i | \(-0.539521\pi\) | ||||
−0.123841 | + | 0.992302i | \(0.539521\pi\) | |||||||
\(440\) | 10.0675 | 0.479951 | ||||||||
\(441\) | 4.21188 | 0.200566 | ||||||||
\(442\) | 6.95425 | 0.330780 | ||||||||
\(443\) | −34.8938 | −1.65786 | −0.828928 | − | 0.559356i | \(-0.811049\pi\) | ||||
−0.828928 | + | 0.559356i | \(0.811049\pi\) | |||||||
\(444\) | 33.2324 | 1.57714 | ||||||||
\(445\) | −14.0744 | −0.667189 | ||||||||
\(446\) | 22.9098 | 1.08481 | ||||||||
\(447\) | −32.4121 | −1.53304 | ||||||||
\(448\) | 13.0483 | 0.616475 | ||||||||
\(449\) | −23.6110 | −1.11427 | −0.557135 | − | 0.830422i | \(-0.688100\pi\) | ||||
−0.557135 | + | 0.830422i | \(0.688100\pi\) | |||||||
\(450\) | −9.51998 | −0.448776 | ||||||||
\(451\) | 22.3244 | 1.05121 | ||||||||
\(452\) | 13.5278 | 0.636296 | ||||||||
\(453\) | 13.9706 | 0.656394 | ||||||||
\(454\) | −35.2235 | −1.65312 | ||||||||
\(455\) | 3.92654 | 0.184079 | ||||||||
\(456\) | −29.3318 | −1.37359 | ||||||||
\(457\) | 25.9758 | 1.21510 | 0.607549 | − | 0.794282i | \(-0.292153\pi\) | ||||
0.607549 | + | 0.794282i | \(0.292153\pi\) | |||||||
\(458\) | −2.26027 | −0.105615 | ||||||||
\(459\) | 2.55014 | 0.119030 | ||||||||
\(460\) | 16.6623 | 0.776883 | ||||||||
\(461\) | 1.46273 | 0.0681262 | 0.0340631 | − | 0.999420i | \(-0.489155\pi\) | ||||
0.0340631 | + | 0.999420i | \(0.489155\pi\) | |||||||
\(462\) | −24.3830 | −1.13440 | ||||||||
\(463\) | 15.2207 | 0.707365 | 0.353683 | − | 0.935366i | \(-0.384929\pi\) | ||||
0.353683 | + | 0.935366i | \(0.384929\pi\) | |||||||
\(464\) | −0.232390 | −0.0107884 | ||||||||
\(465\) | −8.86886 | −0.411284 | ||||||||
\(466\) | −34.9556 | −1.61929 | ||||||||
\(467\) | 18.7707 | 0.868605 | 0.434302 | − | 0.900767i | \(-0.356995\pi\) | ||||
0.434302 | + | 0.900767i | \(0.356995\pi\) | |||||||
\(468\) | −51.4140 | −2.37661 | ||||||||
\(469\) | 11.6655 | 0.538661 | ||||||||
\(470\) | 8.14058 | 0.375497 | ||||||||
\(471\) | −47.9543 | −2.20962 | ||||||||
\(472\) | −3.46855 | −0.159653 | ||||||||
\(473\) | 38.6624 | 1.77770 | ||||||||
\(474\) | −56.8678 | −2.61202 | ||||||||
\(475\) | 4.35807 | 0.199962 | ||||||||
\(476\) | −2.43599 | −0.111653 | ||||||||
\(477\) | −26.1681 | −1.19815 | ||||||||
\(478\) | 40.2451 | 1.84077 | ||||||||
\(479\) | 18.4807 | 0.844407 | 0.422203 | − | 0.906501i | \(-0.361257\pi\) | ||||
0.422203 | + | 0.906501i | \(0.361257\pi\) | |||||||
\(480\) | 16.8169 | 0.767583 | ||||||||
\(481\) | −15.6298 | −0.712656 | ||||||||
\(482\) | 9.11756 | 0.415294 | ||||||||
\(483\) | −14.3934 | −0.654922 | ||||||||
\(484\) | 15.9680 | 0.725817 | ||||||||
\(485\) | 4.45892 | 0.202469 | ||||||||
\(486\) | 45.7149 | 2.07367 | ||||||||
\(487\) | 12.5008 | 0.566466 | 0.283233 | − | 0.959051i | \(-0.408593\pi\) | ||||
0.283233 | + | 0.959051i | \(0.408593\pi\) | |||||||
\(488\) | −14.0573 | −0.636346 | ||||||||
\(489\) | −6.08559 | −0.275200 | ||||||||
\(490\) | −2.26027 | −0.102109 | ||||||||
\(491\) | −25.5151 | −1.15148 | −0.575740 | − | 0.817633i | \(-0.695286\pi\) | ||||
−0.575740 | + | 0.817633i | \(0.695286\pi\) | |||||||
\(492\) | −46.3977 | −2.09177 | ||||||||
\(493\) | 0.329354 | 0.0148333 | ||||||||
\(494\) | 38.6780 | 1.74021 | ||||||||
\(495\) | −16.9191 | −0.760459 | ||||||||
\(496\) | 1.82591 | 0.0819856 | ||||||||
\(497\) | 7.98094 | 0.357994 | ||||||||
\(498\) | 37.1989 | 1.66692 | ||||||||
\(499\) | 35.7307 | 1.59953 | 0.799763 | − | 0.600316i | \(-0.204959\pi\) | ||||
0.799763 | + | 0.600316i | \(0.204959\pi\) | |||||||
\(500\) | 3.10882 | 0.139031 | ||||||||
\(501\) | 39.1773 | 1.75031 | ||||||||
\(502\) | 13.2496 | 0.591360 | ||||||||
\(503\) | 1.34647 | 0.0600359 | 0.0300180 | − | 0.999549i | \(-0.490444\pi\) | ||||
0.0300180 | + | 0.999549i | \(0.490444\pi\) | |||||||
\(504\) | 10.5559 | 0.470198 | ||||||||
\(505\) | 5.22163 | 0.232360 | ||||||||
\(506\) | 48.6634 | 2.16335 | ||||||||
\(507\) | 6.49275 | 0.288353 | ||||||||
\(508\) | 37.1092 | 1.64645 | ||||||||
\(509\) | −24.3580 | −1.07965 | −0.539825 | − | 0.841777i | \(-0.681510\pi\) | ||||
−0.539825 | + | 0.841777i | \(0.681510\pi\) | |||||||
\(510\) | −4.75625 | −0.210610 | ||||||||
\(511\) | −8.23419 | −0.364259 | ||||||||
\(512\) | −6.23355 | −0.275486 | ||||||||
\(513\) | 14.1833 | 0.626208 | ||||||||
\(514\) | −61.5373 | −2.71429 | ||||||||
\(515\) | −8.15389 | −0.359303 | ||||||||
\(516\) | −80.3538 | −3.53738 | ||||||||
\(517\) | 14.4676 | 0.636286 | ||||||||
\(518\) | 8.99711 | 0.395310 | ||||||||
\(519\) | −20.7282 | −0.909867 | ||||||||
\(520\) | 9.84081 | 0.431548 | ||||||||
\(521\) | 0.602173 | 0.0263817 | 0.0131908 | − | 0.999913i | \(-0.495801\pi\) | ||||
0.0131908 | + | 0.999913i | \(0.495801\pi\) | |||||||
\(522\) | −4.00146 | −0.175139 | ||||||||
\(523\) | 2.19000 | 0.0957619 | 0.0478809 | − | 0.998853i | \(-0.484753\pi\) | ||||
0.0478809 | + | 0.998853i | \(0.484753\pi\) | |||||||
\(524\) | 6.71659 | 0.293416 | ||||||||
\(525\) | −2.68549 | −0.117205 | ||||||||
\(526\) | 11.7592 | 0.512724 | ||||||||
\(527\) | −2.58776 | −0.112725 | ||||||||
\(528\) | 5.96433 | 0.259564 | ||||||||
\(529\) | 5.72622 | 0.248966 | ||||||||
\(530\) | 14.0429 | 0.609984 | ||||||||
\(531\) | 5.82912 | 0.252962 | ||||||||
\(532\) | −13.5484 | −0.587399 | ||||||||
\(533\) | 21.8216 | 0.945198 | ||||||||
\(534\) | 85.4306 | 3.69694 | ||||||||
\(535\) | 7.51255 | 0.324796 | ||||||||
\(536\) | 29.2363 | 1.26282 | ||||||||
\(537\) | 57.0106 | 2.46019 | ||||||||
\(538\) | −62.9451 | −2.71376 | ||||||||
\(539\) | −4.01701 | −0.173025 | ||||||||
\(540\) | 10.1176 | 0.435393 | ||||||||
\(541\) | 19.4721 | 0.837171 | 0.418586 | − | 0.908177i | \(-0.362526\pi\) | ||||
0.418586 | + | 0.908177i | \(0.362526\pi\) | |||||||
\(542\) | 58.8271 | 2.52684 | ||||||||
\(543\) | −16.5642 | −0.710838 | ||||||||
\(544\) | 4.90684 | 0.210379 | ||||||||
\(545\) | −8.18571 | −0.350637 | ||||||||
\(546\) | −23.8339 | −1.02000 | ||||||||
\(547\) | 13.2108 | 0.564852 | 0.282426 | − | 0.959289i | \(-0.408861\pi\) | ||||
0.282426 | + | 0.959289i | \(0.408861\pi\) | |||||||
\(548\) | −50.8958 | −2.17416 | ||||||||
\(549\) | 23.6243 | 1.00826 | ||||||||
\(550\) | 9.07952 | 0.387152 | ||||||||
\(551\) | 1.83179 | 0.0780369 | ||||||||
\(552\) | −36.0731 | −1.53538 | ||||||||
\(553\) | −9.36876 | −0.398400 | ||||||||
\(554\) | 53.2209 | 2.26114 | ||||||||
\(555\) | 10.6897 | 0.453754 | ||||||||
\(556\) | −0.162963 | −0.00691118 | ||||||||
\(557\) | 25.2330 | 1.06916 | 0.534578 | − | 0.845119i | \(-0.320471\pi\) | ||||
0.534578 | + | 0.845119i | \(0.320471\pi\) | |||||||
\(558\) | 31.4398 | 1.33095 | ||||||||
\(559\) | 37.7917 | 1.59842 | ||||||||
\(560\) | 0.552885 | 0.0233637 | ||||||||
\(561\) | −8.45293 | −0.356883 | ||||||||
\(562\) | −18.4941 | −0.780128 | ||||||||
\(563\) | 14.3244 | 0.603702 | 0.301851 | − | 0.953355i | \(-0.402395\pi\) | ||||
0.301851 | + | 0.953355i | \(0.402395\pi\) | |||||||
\(564\) | −30.0687 | −1.26612 | ||||||||
\(565\) | 4.35144 | 0.183067 | ||||||||
\(566\) | −44.1876 | −1.85734 | ||||||||
\(567\) | 3.89572 | 0.163605 | ||||||||
\(568\) | 20.0021 | 0.839268 | ||||||||
\(569\) | 17.4857 | 0.733040 | 0.366520 | − | 0.930410i | \(-0.380549\pi\) | ||||
0.366520 | + | 0.930410i | \(0.380549\pi\) | |||||||
\(570\) | −26.4532 | −1.10800 | ||||||||
\(571\) | 31.6774 | 1.32566 | 0.662829 | − | 0.748771i | \(-0.269356\pi\) | ||||
0.662829 | + | 0.748771i | \(0.269356\pi\) | |||||||
\(572\) | 49.0352 | 2.05026 | ||||||||
\(573\) | −37.4066 | −1.56268 | ||||||||
\(574\) | −12.5614 | −0.524301 | ||||||||
\(575\) | 5.35968 | 0.223514 | ||||||||
\(576\) | −54.9579 | −2.28991 | ||||||||
\(577\) | −17.1514 | −0.714023 | −0.357012 | − | 0.934100i | \(-0.616204\pi\) | ||||
−0.357012 | + | 0.934100i | \(0.616204\pi\) | |||||||
\(578\) | 37.0368 | 1.54053 | ||||||||
\(579\) | −44.0830 | −1.83203 | ||||||||
\(580\) | 1.30670 | 0.0542580 | ||||||||
\(581\) | 6.12838 | 0.254248 | ||||||||
\(582\) | −27.0654 | −1.12190 | ||||||||
\(583\) | 24.9574 | 1.03363 | ||||||||
\(584\) | −20.6367 | −0.853955 | ||||||||
\(585\) | −16.5381 | −0.683766 | ||||||||
\(586\) | −7.89046 | −0.325952 | ||||||||
\(587\) | 22.4334 | 0.925924 | 0.462962 | − | 0.886378i | \(-0.346787\pi\) | ||||
0.462962 | + | 0.886378i | \(0.346787\pi\) | |||||||
\(588\) | 8.34871 | 0.344295 | ||||||||
\(589\) | −14.3925 | −0.593035 | ||||||||
\(590\) | −3.12815 | −0.128784 | ||||||||
\(591\) | 28.5007 | 1.17236 | ||||||||
\(592\) | −2.20078 | −0.0904517 | ||||||||
\(593\) | 15.9240 | 0.653921 | 0.326960 | − | 0.945038i | \(-0.393976\pi\) | ||||
0.326960 | + | 0.945038i | \(0.393976\pi\) | |||||||
\(594\) | 29.5492 | 1.21242 | ||||||||
\(595\) | −0.783575 | −0.0321234 | ||||||||
\(596\) | −37.5213 | −1.53693 | ||||||||
\(597\) | −61.9259 | −2.53446 | ||||||||
\(598\) | 47.5674 | 1.94518 | ||||||||
\(599\) | 32.6641 | 1.33462 | 0.667309 | − | 0.744781i | \(-0.267446\pi\) | ||||
0.667309 | + | 0.744781i | \(0.267446\pi\) | |||||||
\(600\) | −6.73046 | −0.274770 | ||||||||
\(601\) | −45.9652 | −1.87496 | −0.937480 | − | 0.348038i | \(-0.886848\pi\) | ||||
−0.937480 | + | 0.348038i | \(0.886848\pi\) | |||||||
\(602\) | −21.7544 | −0.886643 | ||||||||
\(603\) | −49.1335 | −2.00087 | ||||||||
\(604\) | 16.1728 | 0.658061 | ||||||||
\(605\) | 5.13635 | 0.208822 | ||||||||
\(606\) | −31.6950 | −1.28752 | ||||||||
\(607\) | 11.2228 | 0.455518 | 0.227759 | − | 0.973717i | \(-0.426860\pi\) | ||||
0.227759 | + | 0.973717i | \(0.426860\pi\) | |||||||
\(608\) | 27.2908 | 1.10679 | ||||||||
\(609\) | −1.12877 | −0.0457402 | ||||||||
\(610\) | −12.6778 | −0.513308 | ||||||||
\(611\) | 14.1418 | 0.572117 | ||||||||
\(612\) | 10.2601 | 0.414740 | ||||||||
\(613\) | −25.3027 | −1.02197 | −0.510984 | − | 0.859590i | \(-0.670719\pi\) | ||||
−0.510984 | + | 0.859590i | \(0.670719\pi\) | |||||||
\(614\) | 57.9626 | 2.33918 | ||||||||
\(615\) | −14.9245 | −0.601815 | ||||||||
\(616\) | −10.0675 | −0.405633 | ||||||||
\(617\) | 35.1899 | 1.41669 | 0.708347 | − | 0.705864i | \(-0.249441\pi\) | ||||
0.708347 | + | 0.705864i | \(0.249441\pi\) | |||||||
\(618\) | 49.4936 | 1.99093 | ||||||||
\(619\) | −25.7696 | −1.03577 | −0.517884 | − | 0.855451i | \(-0.673280\pi\) | ||||
−0.517884 | + | 0.855451i | \(0.673280\pi\) | |||||||
\(620\) | −10.2669 | −0.412328 | ||||||||
\(621\) | 17.4430 | 0.699965 | ||||||||
\(622\) | 71.3940 | 2.86264 | ||||||||
\(623\) | 14.0744 | 0.563878 | ||||||||
\(624\) | 5.83001 | 0.233387 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −7.05210 | −0.281859 | ||||||||
\(627\) | −47.0133 | −1.87753 | ||||||||
\(628\) | −55.5135 | −2.21523 | ||||||||
\(629\) | 3.11906 | 0.124365 | ||||||||
\(630\) | 9.51998 | 0.379285 | ||||||||
\(631\) | 11.7435 | 0.467501 | 0.233751 | − | 0.972297i | \(-0.424900\pi\) | ||||
0.233751 | + | 0.972297i | \(0.424900\pi\) | |||||||
\(632\) | −23.4803 | −0.933994 | ||||||||
\(633\) | 17.5895 | 0.699119 | ||||||||
\(634\) | 79.8235 | 3.17020 | ||||||||
\(635\) | 11.9367 | 0.473695 | ||||||||
\(636\) | −51.8699 | −2.05678 | ||||||||
\(637\) | −3.92654 | −0.155575 | ||||||||
\(638\) | 3.81632 | 0.151090 | ||||||||
\(639\) | −33.6147 | −1.32978 | ||||||||
\(640\) | 16.9685 | 0.670738 | ||||||||
\(641\) | −18.0951 | −0.714715 | −0.357358 | − | 0.933968i | \(-0.616322\pi\) | ||||
−0.357358 | + | 0.933968i | \(0.616322\pi\) | |||||||
\(642\) | −45.6007 | −1.79972 | ||||||||
\(643\) | −15.3032 | −0.603499 | −0.301749 | − | 0.953387i | \(-0.597571\pi\) | ||||
−0.301749 | + | 0.953387i | \(0.597571\pi\) | |||||||
\(644\) | −16.6623 | −0.656586 | ||||||||
\(645\) | −25.8470 | −1.01773 | ||||||||
\(646\) | −7.71853 | −0.303682 | ||||||||
\(647\) | −21.5323 | −0.846522 | −0.423261 | − | 0.906008i | \(-0.639115\pi\) | ||||
−0.423261 | + | 0.906008i | \(0.639115\pi\) | |||||||
\(648\) | 9.76356 | 0.383549 | ||||||||
\(649\) | −5.55943 | −0.218227 | ||||||||
\(650\) | 8.87504 | 0.348108 | ||||||||
\(651\) | 8.86886 | 0.347598 | ||||||||
\(652\) | −7.04488 | −0.275899 | ||||||||
\(653\) | −21.8937 | −0.856768 | −0.428384 | − | 0.903597i | \(-0.640917\pi\) | ||||
−0.428384 | + | 0.903597i | \(0.640917\pi\) | |||||||
\(654\) | 49.6868 | 1.94291 | ||||||||
\(655\) | 2.16050 | 0.0844176 | ||||||||
\(656\) | 3.07264 | 0.119966 | ||||||||
\(657\) | 34.6814 | 1.35305 | ||||||||
\(658\) | −8.14058 | −0.317353 | ||||||||
\(659\) | −5.20675 | −0.202826 | −0.101413 | − | 0.994844i | \(-0.532336\pi\) | ||||
−0.101413 | + | 0.994844i | \(0.532336\pi\) | |||||||
\(660\) | −33.5368 | −1.30542 | ||||||||
\(661\) | 28.8509 | 1.12217 | 0.561084 | − | 0.827759i | \(-0.310384\pi\) | ||||
0.561084 | + | 0.827759i | \(0.310384\pi\) | |||||||
\(662\) | 30.4452 | 1.18329 | ||||||||
\(663\) | −8.26256 | −0.320891 | ||||||||
\(664\) | 15.3591 | 0.596050 | ||||||||
\(665\) | −4.35807 | −0.168999 | ||||||||
\(666\) | −37.8947 | −1.46839 | ||||||||
\(667\) | 2.25279 | 0.0872285 | ||||||||
\(668\) | 45.3529 | 1.75476 | ||||||||
\(669\) | −27.2198 | −1.05238 | ||||||||
\(670\) | 26.3671 | 1.01865 | ||||||||
\(671\) | −22.5313 | −0.869809 | ||||||||
\(672\) | −16.8169 | −0.648726 | ||||||||
\(673\) | −23.1594 | −0.892730 | −0.446365 | − | 0.894851i | \(-0.647282\pi\) | ||||
−0.446365 | + | 0.894851i | \(0.647282\pi\) | |||||||
\(674\) | 43.1351 | 1.66150 | ||||||||
\(675\) | 3.25449 | 0.125265 | ||||||||
\(676\) | 7.51623 | 0.289086 | ||||||||
\(677\) | 11.1497 | 0.428516 | 0.214258 | − | 0.976777i | \(-0.431267\pi\) | ||||
0.214258 | + | 0.976777i | \(0.431267\pi\) | |||||||
\(678\) | −26.4130 | −1.01439 | ||||||||
\(679\) | −4.45892 | −0.171118 | ||||||||
\(680\) | −1.96382 | −0.0753089 | ||||||||
\(681\) | 41.8501 | 1.60370 | ||||||||
\(682\) | −29.9852 | −1.14819 | ||||||||
\(683\) | 2.69239 | 0.103021 | 0.0515106 | − | 0.998672i | \(-0.483596\pi\) | ||||
0.0515106 | + | 0.998672i | \(0.483596\pi\) | |||||||
\(684\) | 57.0644 | 2.18191 | ||||||||
\(685\) | −16.3714 | −0.625520 | ||||||||
\(686\) | 2.26027 | 0.0862975 | ||||||||
\(687\) | 2.68549 | 0.102458 | ||||||||
\(688\) | 5.32135 | 0.202874 | ||||||||
\(689\) | 24.3953 | 0.929387 | ||||||||
\(690\) | −32.5330 | −1.23851 | ||||||||
\(691\) | −20.0300 | −0.761977 | −0.380989 | − | 0.924580i | \(-0.624416\pi\) | ||||
−0.380989 | + | 0.924580i | \(0.624416\pi\) | |||||||
\(692\) | −23.9957 | −0.912178 | ||||||||
\(693\) | 16.9191 | 0.642705 | ||||||||
\(694\) | −10.6383 | −0.403826 | ||||||||
\(695\) | −0.0524197 | −0.00198839 | ||||||||
\(696\) | −2.82896 | −0.107231 | ||||||||
\(697\) | −4.35469 | −0.164946 | ||||||||
\(698\) | 52.6578 | 1.99313 | ||||||||
\(699\) | 41.5318 | 1.57088 | ||||||||
\(700\) | −3.10882 | −0.117502 | ||||||||
\(701\) | −30.0091 | −1.13343 | −0.566714 | − | 0.823915i | \(-0.691785\pi\) | ||||
−0.566714 | + | 0.823915i | \(0.691785\pi\) | |||||||
\(702\) | 28.8837 | 1.09015 | ||||||||
\(703\) | 17.3475 | 0.654273 | ||||||||
\(704\) | 52.4152 | 1.97547 | ||||||||
\(705\) | −9.67207 | −0.364271 | ||||||||
\(706\) | −25.4499 | −0.957820 | ||||||||
\(707\) | −5.22163 | −0.196380 | ||||||||
\(708\) | 11.5544 | 0.434240 | ||||||||
\(709\) | −14.0856 | −0.528995 | −0.264497 | − | 0.964386i | \(-0.585206\pi\) | ||||
−0.264497 | + | 0.964386i | \(0.585206\pi\) | |||||||
\(710\) | 18.0391 | 0.676994 | ||||||||
\(711\) | 39.4601 | 1.47987 | ||||||||
\(712\) | 35.2736 | 1.32193 | ||||||||
\(713\) | −17.7004 | −0.662885 | ||||||||
\(714\) | 4.75625 | 0.177998 | ||||||||
\(715\) | 15.7729 | 0.589874 | ||||||||
\(716\) | 65.9974 | 2.46644 | ||||||||
\(717\) | −47.8164 | −1.78573 | ||||||||
\(718\) | −38.1522 | −1.42383 | ||||||||
\(719\) | −14.6438 | −0.546122 | −0.273061 | − | 0.961997i | \(-0.588036\pi\) | ||||
−0.273061 | + | 0.961997i | \(0.588036\pi\) | |||||||
\(720\) | −2.32868 | −0.0867849 | ||||||||
\(721\) | 8.15389 | 0.303667 | ||||||||
\(722\) | 0.0163668 | 0.000609109 0 | ||||||||
\(723\) | −10.8328 | −0.402878 | ||||||||
\(724\) | −19.1753 | −0.712643 | ||||||||
\(725\) | 0.420322 | 0.0156104 | ||||||||
\(726\) | −31.1773 | −1.15710 | ||||||||
\(727\) | −3.86159 | −0.143218 | −0.0716092 | − | 0.997433i | \(-0.522813\pi\) | ||||
−0.0716092 | + | 0.997433i | \(0.522813\pi\) | |||||||
\(728\) | −9.84081 | −0.364725 | ||||||||
\(729\) | −42.6280 | −1.57882 | ||||||||
\(730\) | −18.6115 | −0.688842 | ||||||||
\(731\) | −7.54166 | −0.278938 | ||||||||
\(732\) | 46.8276 | 1.73080 | ||||||||
\(733\) | −0.843881 | −0.0311695 | −0.0155847 | − | 0.999879i | \(-0.504961\pi\) | ||||
−0.0155847 | + | 0.999879i | \(0.504961\pi\) | |||||||
\(734\) | 29.4989 | 1.08882 | ||||||||
\(735\) | 2.68549 | 0.0990559 | ||||||||
\(736\) | 33.5630 | 1.23715 | ||||||||
\(737\) | 46.8603 | 1.72612 | ||||||||
\(738\) | 52.9069 | 1.94753 | ||||||||
\(739\) | 16.7430 | 0.615902 | 0.307951 | − | 0.951402i | \(-0.400357\pi\) | ||||
0.307951 | + | 0.951402i | \(0.400357\pi\) | |||||||
\(740\) | 12.3748 | 0.454907 | ||||||||
\(741\) | −45.9545 | −1.68818 | ||||||||
\(742\) | −14.0429 | −0.515531 | ||||||||
\(743\) | 43.2671 | 1.58732 | 0.793658 | − | 0.608364i | \(-0.208174\pi\) | ||||
0.793658 | + | 0.608364i | \(0.208174\pi\) | |||||||
\(744\) | 22.2274 | 0.814896 | ||||||||
\(745\) | −12.0693 | −0.442186 | ||||||||
\(746\) | 18.5943 | 0.680785 | ||||||||
\(747\) | −25.8120 | −0.944411 | ||||||||
\(748\) | −9.78539 | −0.357789 | ||||||||
\(749\) | −7.51255 | −0.274503 | ||||||||
\(750\) | −6.06994 | −0.221643 | ||||||||
\(751\) | 23.0952 | 0.842756 | 0.421378 | − | 0.906885i | \(-0.361547\pi\) | ||||
0.421378 | + | 0.906885i | \(0.361547\pi\) | |||||||
\(752\) | 1.99127 | 0.0726141 | ||||||||
\(753\) | −15.7423 | −0.573681 | ||||||||
\(754\) | 3.73037 | 0.135852 | ||||||||
\(755\) | 5.20223 | 0.189329 | ||||||||
\(756\) | −10.1176 | −0.367974 | ||||||||
\(757\) | 46.0148 | 1.67244 | 0.836218 | − | 0.548397i | \(-0.184762\pi\) | ||||
0.836218 | + | 0.548397i | \(0.184762\pi\) | |||||||
\(758\) | 33.8966 | 1.23118 | ||||||||
\(759\) | −57.8184 | −2.09867 | ||||||||
\(760\) | −10.9223 | −0.396194 | ||||||||
\(761\) | −36.5677 | −1.32558 | −0.662789 | − | 0.748806i | \(-0.730627\pi\) | ||||
−0.662789 | + | 0.748806i | \(0.730627\pi\) | |||||||
\(762\) | −72.4553 | −2.62478 | ||||||||
\(763\) | 8.18571 | 0.296343 | ||||||||
\(764\) | −43.3031 | −1.56665 | ||||||||
\(765\) | 3.30032 | 0.119323 | ||||||||
\(766\) | −13.4636 | −0.486459 | ||||||||
\(767\) | −5.43422 | −0.196218 | ||||||||
\(768\) | −32.9152 | −1.18773 | ||||||||
\(769\) | −18.2031 | −0.656421 | −0.328210 | − | 0.944605i | \(-0.606445\pi\) | ||||
−0.328210 | + | 0.944605i | \(0.606445\pi\) | |||||||
\(770\) | −9.07952 | −0.327203 | ||||||||
\(771\) | 73.1143 | 2.63315 | ||||||||
\(772\) | −51.0320 | −1.83668 | ||||||||
\(773\) | 53.3680 | 1.91951 | 0.959756 | − | 0.280835i | \(-0.0906114\pi\) | ||||
0.959756 | + | 0.280835i | \(0.0906114\pi\) | |||||||
\(774\) | 91.6268 | 3.29346 | ||||||||
\(775\) | −3.30251 | −0.118630 | ||||||||
\(776\) | −11.1751 | −0.401162 | ||||||||
\(777\) | −10.6897 | −0.383492 | ||||||||
\(778\) | −21.0955 | −0.756311 | ||||||||
\(779\) | −24.2198 | −0.867764 | ||||||||
\(780\) | −32.7816 | −1.17377 | ||||||||
\(781\) | 32.0595 | 1.14718 | ||||||||
\(782\) | −9.49248 | −0.339450 | ||||||||
\(783\) | 1.36793 | 0.0488860 | ||||||||
\(784\) | −0.552885 | −0.0197459 | ||||||||
\(785\) | −17.8568 | −0.637336 | ||||||||
\(786\) | −13.1141 | −0.467764 | ||||||||
\(787\) | −6.28335 | −0.223977 | −0.111989 | − | 0.993709i | \(-0.535722\pi\) | ||||
−0.111989 | + | 0.993709i | \(0.535722\pi\) | |||||||
\(788\) | 32.9934 | 1.17534 | ||||||||
\(789\) | −13.9714 | −0.497396 | ||||||||
\(790\) | −21.1759 | −0.753405 | ||||||||
\(791\) | −4.35144 | −0.154720 | ||||||||
\(792\) | 42.4032 | 1.50673 | ||||||||
\(793\) | −22.0238 | −0.782089 | ||||||||
\(794\) | 51.9985 | 1.84536 | ||||||||
\(795\) | −16.6848 | −0.591748 | ||||||||
\(796\) | −71.6876 | −2.54090 | ||||||||
\(797\) | −25.7280 | −0.911333 | −0.455667 | − | 0.890150i | \(-0.650599\pi\) | ||||
−0.455667 | + | 0.890150i | \(0.650599\pi\) | |||||||
\(798\) | 26.4532 | 0.936434 | ||||||||
\(799\) | −2.82212 | −0.0998394 | ||||||||
\(800\) | 6.26213 | 0.221400 | ||||||||
\(801\) | −59.2795 | −2.09454 | ||||||||
\(802\) | −5.87451 | −0.207436 | ||||||||
\(803\) | −33.0768 | −1.16725 | ||||||||
\(804\) | −97.3916 | −3.43474 | ||||||||
\(805\) | −5.35968 | −0.188904 | ||||||||
\(806\) | −29.3099 | −1.03240 | ||||||||
\(807\) | 74.7870 | 2.63263 | ||||||||
\(808\) | −13.0866 | −0.460385 | ||||||||
\(809\) | 10.1336 | 0.356279 | 0.178139 | − | 0.984005i | \(-0.442992\pi\) | ||||
0.178139 | + | 0.984005i | \(0.442992\pi\) | |||||||
\(810\) | 8.80537 | 0.309389 | ||||||||
\(811\) | −45.5649 | −1.60000 | −0.800000 | − | 0.600000i | \(-0.795167\pi\) | ||||
−0.800000 | + | 0.600000i | \(0.795167\pi\) | |||||||
\(812\) | −1.30670 | −0.0458563 | ||||||||
\(813\) | −69.8942 | −2.45130 | ||||||||
\(814\) | 36.1415 | 1.26676 | ||||||||
\(815\) | −2.26610 | −0.0793779 | ||||||||
\(816\) | −1.16343 | −0.0407281 | ||||||||
\(817\) | −41.9450 | −1.46747 | ||||||||
\(818\) | 14.1622 | 0.495168 | ||||||||
\(819\) | 16.5381 | 0.577888 | ||||||||
\(820\) | −17.2771 | −0.603344 | ||||||||
\(821\) | −25.6724 | −0.895974 | −0.447987 | − | 0.894040i | \(-0.647859\pi\) | ||||
−0.447987 | + | 0.894040i | \(0.647859\pi\) | |||||||
\(822\) | 99.3736 | 3.46605 | ||||||||
\(823\) | 42.4999 | 1.48145 | 0.740727 | − | 0.671806i | \(-0.234481\pi\) | ||||
0.740727 | + | 0.671806i | \(0.234481\pi\) | |||||||
\(824\) | 20.4355 | 0.711905 | ||||||||
\(825\) | −10.7876 | −0.375578 | ||||||||
\(826\) | 3.12815 | 0.108842 | ||||||||
\(827\) | −18.3140 | −0.636841 | −0.318421 | − | 0.947950i | \(-0.603152\pi\) | ||||
−0.318421 | + | 0.947950i | \(0.603152\pi\) | |||||||
\(828\) | 70.1795 | 2.43891 | ||||||||
\(829\) | −41.0348 | −1.42520 | −0.712599 | − | 0.701572i | \(-0.752482\pi\) | ||||
−0.712599 | + | 0.701572i | \(0.752482\pi\) | |||||||
\(830\) | 13.8518 | 0.480803 | ||||||||
\(831\) | −63.2334 | −2.19354 | ||||||||
\(832\) | 51.2348 | 1.77625 | ||||||||
\(833\) | 0.783575 | 0.0271493 | ||||||||
\(834\) | 0.318184 | 0.0110178 | ||||||||
\(835\) | 14.5885 | 0.504855 | ||||||||
\(836\) | −54.4242 | −1.88230 | ||||||||
\(837\) | −10.7480 | −0.371504 | ||||||||
\(838\) | 24.3958 | 0.842739 | ||||||||
\(839\) | 11.1918 | 0.386385 | 0.193192 | − | 0.981161i | \(-0.438116\pi\) | ||||
0.193192 | + | 0.981161i | \(0.438116\pi\) | |||||||
\(840\) | 6.73046 | 0.232223 | ||||||||
\(841\) | −28.8233 | −0.993908 | ||||||||
\(842\) | −46.2530 | −1.59398 | ||||||||
\(843\) | 21.9734 | 0.756806 | ||||||||
\(844\) | 20.3622 | 0.700895 | ||||||||
\(845\) | 2.41771 | 0.0831719 | ||||||||
\(846\) | 34.2871 | 1.17882 | ||||||||
\(847\) | −5.13635 | −0.176487 | ||||||||
\(848\) | 3.43503 | 0.117960 | ||||||||
\(849\) | 52.5006 | 1.80182 | ||||||||
\(850\) | −1.77109 | −0.0607479 | ||||||||
\(851\) | 21.3345 | 0.731336 | ||||||||
\(852\) | −66.6306 | −2.28273 | ||||||||
\(853\) | 46.0029 | 1.57511 | 0.787555 | − | 0.616245i | \(-0.211347\pi\) | ||||
0.787555 | + | 0.616245i | \(0.211347\pi\) | |||||||
\(854\) | 12.6778 | 0.433825 | ||||||||
\(855\) | 18.3557 | 0.627750 | ||||||||
\(856\) | −18.8282 | −0.643534 | ||||||||
\(857\) | 30.1368 | 1.02945 | 0.514726 | − | 0.857355i | \(-0.327894\pi\) | ||||
0.514726 | + | 0.857355i | \(0.327894\pi\) | |||||||
\(858\) | −95.7408 | −3.26854 | ||||||||
\(859\) | −39.4804 | −1.34705 | −0.673526 | − | 0.739163i | \(-0.735221\pi\) | ||||
−0.673526 | + | 0.739163i | \(0.735221\pi\) | |||||||
\(860\) | −29.9214 | −1.02031 | ||||||||
\(861\) | 14.9245 | 0.508627 | ||||||||
\(862\) | −6.67168 | −0.227238 | ||||||||
\(863\) | 47.6629 | 1.62246 | 0.811231 | − | 0.584725i | \(-0.198798\pi\) | ||||
0.811231 | + | 0.584725i | \(0.198798\pi\) | |||||||
\(864\) | 20.3800 | 0.693343 | ||||||||
\(865\) | −7.71858 | −0.262440 | ||||||||
\(866\) | −32.0387 | −1.08872 | ||||||||
\(867\) | −44.0045 | −1.49447 | ||||||||
\(868\) | 10.2669 | 0.348481 | ||||||||
\(869\) | −37.6344 | −1.27666 | ||||||||
\(870\) | −2.55133 | −0.0864982 | ||||||||
\(871\) | 45.8049 | 1.55204 | ||||||||
\(872\) | 20.5153 | 0.694734 | ||||||||
\(873\) | 18.7804 | 0.635622 | ||||||||
\(874\) | −52.7951 | −1.78582 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 68.7449 | 2.32267 | ||||||||
\(877\) | 28.8843 | 0.975353 | 0.487676 | − | 0.873024i | \(-0.337845\pi\) | ||||
0.487676 | + | 0.873024i | \(0.337845\pi\) | |||||||
\(878\) | 11.7297 | 0.395857 | ||||||||
\(879\) | 9.37489 | 0.316207 | ||||||||
\(880\) | 2.22094 | 0.0748680 | ||||||||
\(881\) | −16.4014 | −0.552576 | −0.276288 | − | 0.961075i | \(-0.589104\pi\) | ||||
−0.276288 | + | 0.961075i | \(0.589104\pi\) | |||||||
\(882\) | −9.51998 | −0.320554 | ||||||||
\(883\) | 37.0625 | 1.24725 | 0.623626 | − | 0.781723i | \(-0.285659\pi\) | ||||
0.623626 | + | 0.781723i | \(0.285659\pi\) | |||||||
\(884\) | −9.56502 | −0.321706 | ||||||||
\(885\) | 3.71665 | 0.124934 | ||||||||
\(886\) | 78.8695 | 2.64967 | ||||||||
\(887\) | 9.97662 | 0.334982 | 0.167491 | − | 0.985874i | \(-0.446433\pi\) | ||||
0.167491 | + | 0.985874i | \(0.446433\pi\) | |||||||
\(888\) | −26.7909 | −0.899044 | ||||||||
\(889\) | −11.9367 | −0.400346 | ||||||||
\(890\) | 31.8119 | 1.06634 | ||||||||
\(891\) | 15.6491 | 0.524266 | ||||||||
\(892\) | −31.5106 | −1.05505 | ||||||||
\(893\) | −15.6960 | −0.525247 | ||||||||
\(894\) | 73.2600 | 2.45018 | ||||||||
\(895\) | 21.2291 | 0.709611 | ||||||||
\(896\) | −16.9685 | −0.566877 | ||||||||
\(897\) | −56.5163 | −1.88702 | ||||||||
\(898\) | 53.3672 | 1.78088 | ||||||||
\(899\) | −1.38812 | −0.0462963 | ||||||||
\(900\) | 13.0940 | 0.436465 | ||||||||
\(901\) | −4.86829 | −0.162186 | ||||||||
\(902\) | −50.4591 | −1.68010 | ||||||||
\(903\) | 25.8470 | 0.860136 | ||||||||
\(904\) | −10.9057 | −0.362719 | ||||||||
\(905\) | −6.16803 | −0.205032 | ||||||||
\(906\) | −31.5772 | −1.04908 | ||||||||
\(907\) | −58.9938 | −1.95886 | −0.979428 | − | 0.201794i | \(-0.935323\pi\) | ||||
−0.979428 | + | 0.201794i | \(0.935323\pi\) | |||||||
\(908\) | 48.4471 | 1.60777 | ||||||||
\(909\) | 21.9929 | 0.729458 | ||||||||
\(910\) | −8.87504 | −0.294205 | ||||||||
\(911\) | 14.0114 | 0.464219 | 0.232109 | − | 0.972690i | \(-0.425437\pi\) | ||||
0.232109 | + | 0.972690i | \(0.425437\pi\) | |||||||
\(912\) | −6.47073 | −0.214267 | ||||||||
\(913\) | 24.6177 | 0.814729 | ||||||||
\(914\) | −58.7124 | −1.94203 | ||||||||
\(915\) | 15.0628 | 0.497962 | ||||||||
\(916\) | 3.10882 | 0.102718 | ||||||||
\(917\) | −2.16050 | −0.0713459 | ||||||||
\(918\) | −5.76399 | −0.190240 | ||||||||
\(919\) | 15.1377 | 0.499347 | 0.249674 | − | 0.968330i | \(-0.419677\pi\) | ||||
0.249674 | + | 0.968330i | \(0.419677\pi\) | |||||||
\(920\) | −13.4326 | −0.442859 | ||||||||
\(921\) | −68.8671 | −2.26925 | ||||||||
\(922\) | −3.30617 | −0.108883 | ||||||||
\(923\) | 31.3375 | 1.03149 | ||||||||
\(924\) | 33.5368 | 1.10328 | ||||||||
\(925\) | 3.98055 | 0.130880 | ||||||||
\(926\) | −34.4028 | −1.13055 | ||||||||
\(927\) | −34.3432 | −1.12798 | ||||||||
\(928\) | 2.63211 | 0.0864032 | ||||||||
\(929\) | 36.5377 | 1.19876 | 0.599382 | − | 0.800463i | \(-0.295413\pi\) | ||||
0.599382 | + | 0.800463i | \(0.295413\pi\) | |||||||
\(930\) | 20.0460 | 0.657335 | ||||||||
\(931\) | 4.35807 | 0.142830 | ||||||||
\(932\) | 48.0786 | 1.57487 | ||||||||
\(933\) | −84.8253 | −2.77706 | ||||||||
\(934\) | −42.4269 | −1.38825 | ||||||||
\(935\) | −3.14762 | −0.102938 | ||||||||
\(936\) | 41.4483 | 1.35478 | ||||||||
\(937\) | −32.0419 | −1.04676 | −0.523382 | − | 0.852098i | \(-0.675330\pi\) | ||||
−0.523382 | + | 0.852098i | \(0.675330\pi\) | |||||||
\(938\) | −26.3671 | −0.860916 | ||||||||
\(939\) | 8.37881 | 0.273432 | ||||||||
\(940\) | −11.1967 | −0.365196 | ||||||||
\(941\) | 5.64517 | 0.184027 | 0.0920136 | − | 0.995758i | \(-0.470670\pi\) | ||||
0.0920136 | + | 0.995758i | \(0.470670\pi\) | |||||||
\(942\) | 108.390 | 3.53152 | ||||||||
\(943\) | −29.7862 | −0.969974 | ||||||||
\(944\) | −0.765177 | −0.0249044 | ||||||||
\(945\) | −3.25449 | −0.105869 | ||||||||
\(946\) | −87.3875 | −2.84121 | ||||||||
\(947\) | −40.8786 | −1.32838 | −0.664188 | − | 0.747565i | \(-0.731223\pi\) | ||||
−0.664188 | + | 0.747565i | \(0.731223\pi\) | |||||||
\(948\) | 78.2171 | 2.54037 | ||||||||
\(949\) | −32.3319 | −1.04954 | ||||||||
\(950\) | −9.85041 | −0.319589 | ||||||||
\(951\) | −94.8407 | −3.07542 | ||||||||
\(952\) | 1.96382 | 0.0636477 | ||||||||
\(953\) | −51.3729 | −1.66413 | −0.832066 | − | 0.554676i | \(-0.812842\pi\) | ||||
−0.832066 | + | 0.554676i | \(0.812842\pi\) | |||||||
\(954\) | 59.1469 | 1.91495 | ||||||||
\(955\) | −13.9291 | −0.450736 | ||||||||
\(956\) | −55.3538 | −1.79027 | ||||||||
\(957\) | −4.53429 | −0.146573 | ||||||||
\(958\) | −41.7715 | −1.34957 | ||||||||
\(959\) | 16.3714 | 0.528661 | ||||||||
\(960\) | −35.0412 | −1.13095 | ||||||||
\(961\) | −20.0935 | −0.648176 | ||||||||
\(962\) | 35.3275 | 1.13900 | ||||||||
\(963\) | 31.6419 | 1.01965 | ||||||||
\(964\) | −12.5405 | −0.403901 | ||||||||
\(965\) | −16.4152 | −0.528425 | ||||||||
\(966\) | 32.5330 | 1.04673 | ||||||||
\(967\) | −21.6790 | −0.697149 | −0.348574 | − | 0.937281i | \(-0.613334\pi\) | ||||
−0.348574 | + | 0.937281i | \(0.613334\pi\) | |||||||
\(968\) | −12.8729 | −0.413749 | ||||||||
\(969\) | 9.17062 | 0.294603 | ||||||||
\(970\) | −10.0784 | −0.323597 | ||||||||
\(971\) | −30.3135 | −0.972807 | −0.486403 | − | 0.873734i | \(-0.661691\pi\) | ||||
−0.486403 | + | 0.873734i | \(0.661691\pi\) | |||||||
\(972\) | −62.8771 | −2.01678 | ||||||||
\(973\) | 0.0524197 | 0.00168050 | ||||||||
\(974\) | −28.2552 | −0.905355 | ||||||||
\(975\) | −10.5447 | −0.337701 | ||||||||
\(976\) | −3.10111 | −0.0992642 | ||||||||
\(977\) | −10.5947 | −0.338953 | −0.169477 | − | 0.985534i | \(-0.554208\pi\) | ||||
−0.169477 | + | 0.985534i | \(0.554208\pi\) | |||||||
\(978\) | 13.7551 | 0.439838 | ||||||||
\(979\) | 56.5368 | 1.80693 | ||||||||
\(980\) | 3.10882 | 0.0993076 | ||||||||
\(981\) | −34.4772 | −1.10077 | ||||||||
\(982\) | 57.6710 | 1.84036 | ||||||||
\(983\) | −47.4815 | −1.51442 | −0.757212 | − | 0.653170i | \(-0.773439\pi\) | ||||
−0.757212 | + | 0.653170i | \(0.773439\pi\) | |||||||
\(984\) | 37.4043 | 1.19241 | ||||||||
\(985\) | 10.6128 | 0.338153 | ||||||||
\(986\) | −0.744428 | −0.0237074 | ||||||||
\(987\) | 9.67207 | 0.307865 | ||||||||
\(988\) | −53.1985 | −1.69247 | ||||||||
\(989\) | −51.5853 | −1.64032 | ||||||||
\(990\) | 38.2418 | 1.21540 | ||||||||
\(991\) | −18.9067 | −0.600590 | −0.300295 | − | 0.953846i | \(-0.597085\pi\) | ||||
−0.300295 | + | 0.953846i | \(0.597085\pi\) | |||||||
\(992\) | −20.6807 | −0.656613 | ||||||||
\(993\) | −36.1729 | −1.14791 | ||||||||
\(994\) | −18.0391 | −0.572165 | ||||||||
\(995\) | −23.0594 | −0.731033 | ||||||||
\(996\) | −51.1641 | −1.62120 | ||||||||
\(997\) | 42.9818 | 1.36125 | 0.680623 | − | 0.732634i | \(-0.261709\pi\) | ||||
0.680623 | + | 0.732634i | \(0.261709\pi\) | |||||||
\(998\) | −80.7610 | −2.55644 | ||||||||
\(999\) | 12.9547 | 0.409867 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8015.2.a.i.1.5 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.i.1.5 | ✓ | 44 | 1.1 | even | 1 | trivial |